The Effect of Assuming a Homogeneous Poisson Process When the True Process is a Power Law Process

The homogeneous Poisson process is the simplest model for describing the random occurrence of events in time, such as the failure times of a repairable system. A more complex model, which includes the homogeneous Poisson process as a special case, is the power law process. What is the effect if the simpler homogeneous Poisson process is assumed, when in reality the process is a power law process? In this article, the effect of this erroneous assumption on estimation of the intensity function at the current time is studied. The effects on point and interval estimation are discussed for situations in which the data are either failure truncated or time truncated.